Analysis Of Critical Heat Flux Research Articles

Data-driven dimensional analysis of critical heat flux in subcooled vertical flow: A two-stage machine learning approach

This study presents a novel two-stage machine learning algorithm that identifies dominant dimensionless numbers for critical heat flux (CHF) prediction, circumventing the limitations of traditional dimensional analysis by integrating the Buckingham Pi theorem with advanced computational methods, including the active subspace method and machine learning. When applied to extensive datasets, including 1438 data points from subcooled departure from nucleate boiling (DNB) conditions and validated against a non-overlapping 24,284-point lookup table dataset, our algorithm effectively discerns and validates the dimensionless numbers critical to the CHF phenomena. Notably, it identifies a significant negative correlation between a newly discovered dominant dimensionless number and the boiling number Bochf = q″w,chf / (G hfg), and introduces a new simplified scaling law for water under earth's gravitational conditions, outperforming existing models with substantial predictive accuracy. This scaling law and the identified dimensionless numbers, derived from an initial dataset of 1438 data points, exhibit exceptional generalization capabilities when validated against a significantly larger dataset of 24,284 points. These findings also emphasize the nonlinear effects of inlet quality on the boiling number Bochf. The contribution of this research lies in its potential to deepen the understanding of CHF based on data-driven fashion, with the potential to enhance thermal management and design optimization across various applications.

Subchannel analysis of critical heat flux in radially Non-uniform heated rod assembly at low flow rate

The effect of radial power distribution and low flow rate on critical heat flux (CHF) was investigated. In this study, based on the CHF experimental results of Columbia University, the research validated the feasibility of the subchannel analysis code CTF to predict CHF. The results show that CTF code using the EPRI empirical CHF correlation can predict the CHF experimental results well. Due to radially non-uniform power distribution, the quality and void fraction of hot subchannels are higher than other subchannels. The influence of the lateral flow will cause the counterflow in low power region under the beginning of two-phase flow at low flow rate. Furthermore, the predicted average CHF of rod assembly increases with the increase of inlet mass flow rate and the decrease of inlet temperature. When CHF happens in the rod assembly, the local CHF is mainly due to the low mass flow rate and high quality.

Subchannel Analysis of Critical Heat Flux in Radially Non-Uniform Heated Rod Assembly at Low Flow Rate

Subchannel Analysis of Critical Heat Flux in Radially Non-Uniform Heated Rod Assembly at Low Flow Rate

Calculation and Analysis of Critical Heat Flux at LWR Passive Safety Design

Critical heat flux (MDNBR) is one parameter for safe nuclear reactor operation. The magnitude of MDNBR is determined by local heat flux. When it is sufficiently high, it will cause a change in heat equilibrium and deteriorate nuclear fuel structure. To obtain assurance for nuclear reactor safety in safe criteria, Calculation and analysis of Critical heat flux of 630 MWe passive LWR was carried out at steady state and transient condition. The study used COBRA IV-I sub channel program coupled with critical heat flux correlation of EPRI-Columbia and W-3. The program models the core into 1/8 sections, each of which is divided into 83 sub-channels in radial direction and 40 nodes in axial direction, including 8 sub-channels of the hottest assembly. Normalized coast down flow and reactor power decay at initial phase is 10 second after loss of flow accident (LOFA) caused by anticipated primary pump failure. The effects of all input parameters, such as radial nodes, axial nodes, mix coefficient, velocity of coolant mass entering the core and power variation, have been identified. Evaluation of the results of safety calculation indicates that MDNBR, cladding temperature, and hot channel temperature are 1.83, 349°C and 2033°C, respectively. As the licensing limits for those parameters are 1.3, 1850°C, and 2840°C, it is concluded that the design of 630 MWe passive LWR has met the licensing criteria of safety. Modelling for safety analysis of passive LWR employs COBRA IV-I program. The results show that this program can be used to calculate hydraulic safety parameters with sub-channel model.

The Study of Critical Heat Flux in Upflow Boiling Vertical Round Tube under High Pressure

The Critical Heat Flux (CHF) prediction under high pressure condition, even close to the vicinity of the critical pressure of water, is an important issue. Although there are many empirical CHF correlations, most of them have covered the pressure under 15MPa. In this study, based on the CHF experiment database of upflow boiling in vertical round tube from 15MPa to the vicinity of the critical pressure of water, the Katto, Bowring, Hall-Mudawar, Alekseev correlations, and Groeneveld LUT-2006 are comparatively studied. With an error analysis of the predicted CHF to the experiment database, the prediction capability and the applicability of these correlations are evaluated and the parametric trends of CHF varying with pressure from 15MPa to critical pressure are proposed. Simultaneously, according to the characteristics of Departure from Nucleate Boiling (DNB) type CHF under high pressure condition, the constitutive correlations of Weisman & Pei model are proposed. The prediction results of three entrainment and deposition correlations of Kataoka, Celata, and Hewitt corresponding to the Dry-Out (DO) type CHF are analyzed. Based on the two improved models above, a comprehensive CHF mechanistic model under high pressure condition combining the DNB and DO type CHF is established. The verification based on the experiment database of upflow boiling in vertical round tube and the parametric trends analysis of CHF varying with thermal-hydraulic and geometric parameters are carried out. Findings of this study have a positive effect on further development of CHF prediction method for universal CHF mechanism, especially under high pressure region.

Analysis of critical heat flux under vertical subcooled flow boiling condition (Development and evaluation for prediction method of DNB heat flux under non-uniform axial heat flux condition)

Analysis of critical heat flux under vertical subcooled flow boiling condition (Development and evaluation for prediction method of DNB heat flux under non-uniform axial heat flux condition)

Analysis of CHF in saturated forced convective boiling on a heated surface with impinging jets using artificial neural network and genetic algorithm

In this paper, a three-layer Back Propagation (BP) algorithm artificial neural network (ANN) for predicting critical heat flux (CHF) in saturated forced convective boiling on a heated surface with impinging jets was trained successfully with a root mean square (RMS) error of 17.39%. The input parameters of the ANN are liquid-to-vapor density ratio, ρ l / ρ v , the ratio of characteristic dimension of the heated surface to the diameter of the impinging jet, L/ d, reciprocal of the Weber number, 2 σ/ ρ l u 2( L − d), and the number of impinging jets, N j . The output is dimensionless heat flux, q c o / ρ v H f g u . Based on the trained ANN, the influence of principal parameters on CHF has been analyzed as follows. CHF increases with an increase in jet velocity and decreases with an increase in L/ d and N j . CHF increases with an increase in pressure at first and then decreases. Besides, a new correlation was generalized using genetic algorithm (GA) as a comparison with ANN to confirm the advantage of ANN.

Study on Ex-Vessel Cooling of Reactor Pressure Vessel (Model Analysis of Critical Heat Flux on Inclined Plate and Hemisphere Facing Downward)

Critical heat fluxes (CHFs) on inclined plates and hemispheres in the case of saturated pool boiling were investigated analytically. In the present model, the most dangerous wavelength and propagation velocity in the Kelvin-Helmholtz instability on the liquid-vapor interface were calculated to determine the length and the velocity of the coalesced bubbles at CHF. The time period for which the coalesced bubble covered the heated surface was calculated as the length divided by the velocity. In close to the surface oriented downward, the characteristic length was provided by the length of the heater; the characteristic velocity was given by the correlation of the rising velocity of a spherical cap bubble with 17 to 40 mm the equivalent diameter. The predictions agreed well with previous experimental data obtained for an inclined plate in overall inclination angle. The model given as a function of the inclination angle was developed for the CHF on a hemisphere. The extended model well represented the experimental data on hemispheres.

Assessment of the interchannel mixing model with a subchannel analysis code for BWR and PWR conditions

The influence of the interchannel mixing model employed in a traditional subchannel analysis code was investigated in this study, specifically on the analysis of the enthalpy distribution and critical heat flux (CHF) in rod bundles in BWR and PWR conditions. The equal-volume-exchange turbulent mixing and void drift model (EVVD) was embodied to the COBRA-IV-I code. An optimized model of the void drift coefficient has been devised in this study as the result of the assessment with the two-phase flow distribution data for the general electric (GE) 9-rod and Ispra 16-rod test bundles. The influence of the subchannel analysis model on the analysis of CHF was examined by evaluating the CHF test data in rod bundles representing PWR and BWR conditions. The CHFR margins of typical light water nuclear reactor (LWR) cores were evaluated by considering the influence on the local parameter CHF correlation and the hot channel analysis result. It appeared that the interchannel mixing model has an important effect upon the analysis of CHFR margin for BWR conditions.

Critical heat flux at high velocity channel flow with high subcooling

A quantitative analysis of critical heat flux (CHF) in heated channels under high mass flux with high subcooling was successfully carried out by applying a new flow model to the existing CHF model of a macro-water-sublayer on the heated wall and steam blankets over it. The CHF correlation proposed could correctly predict the existing experimental data for circular tubes of 0.33–4 mm in diameter with mass flux of 124–90 000 kg (m 2 s) −1 and inlet water subcooling of 35–210 K at 0.1–7.1 MPa, resulting in CHF of 4.2–224 MW m −2, and for rectangular channels of 3–20 mm gap with a mass flux of 940–27 000 kg (m 2 s) −1 and inlet water subcooling of 13–166 K at 0.1–3.0 MPa, resulting in CHF of 2.0–62 MW m −2. An error of the CHF correlation has also been estimated.

Dimensional analysis of critical heat flux in subcooled water flow under one-side heating conditions for fusion application

Critical heat flux (CHF) experiments have been carried out to design a high performance cooling device with pressurized subcooled water flow under one-side heating conditions for plasma facing components. Swirl, screw and hypervapotron tubes are the most efficient geometries to remove high incident heat fluxes. A dimensional analysis shows that CHF phenomenon can be featured by dimensionless groups that are the critical Boiling, the Eckert and the Reynolds numbers, the mass enthalpic quality and the ratio between liquid and vapor densities. CHF for uniformly heated smooth tubes, the maximum wall heat flux for smooth and for swirl tubes under one-side heating conditions are predicted with a reasonable accuracy by correlating these five dimensionless groups. An enhancement factor featuring the difference between one-side and uniform heating is also introduced. CHF occurrence under one-side heating is characterized by a normalized temperature, ratio between the maximal wall temperature and the onset of nucleate boiling temperature, which only depends on the pressure. According to finite element calculations performed for smooth and swirl tubes, temperature and heat flux are distributed along the inner wall of the cooling channel under one-side heating conditions. These distributions are characterized by two dimensionless numbers for each geometry: a peaking factor, which is the ratio between the maximal heat flux at the inner wall of the cooling channel and the incident heat flux, and a full width angle at half maximum of wall heat flux at the inner wall of the cooling channel. This study draws the dimensionless groups featuring CHF phenomenon not only under uniform heating, but also under one-side heating, which involve additional normalized parameters.

Critical heat flux under conditions of high subcooling and high velocity at atmospheric pressure

A quantitative analysis of critical heat flux (CHF) under high mass flux with high subcooling at atmospheric pressure was successfully carried out by applying a new transition region model for a macro-water sublayer on heated walls to the existing model of a vapor blanket over the macro-water sublayer. The CHF correlation proposed in this study could predict well the experimental data obtained for water mass flux of 940 to 20,300 kg/m2s using circulate tubes 2 to 4 mm in diameter and 30 to 100 mm in length with inlet subcooling of 30 to 90 °C and rectangular channels heated from one side with gaps of 3 to 20 mm, length of 50 to 305 mm, and inlet subcooling of 30 to 77 °C and revealed a unique feature of CHF, namely, that the effects of wall friction of subcooled boiling flow and the velocity of the steam blanket above the macro-water sublayer at atmospheric pressure become the dominant factors while they were not dominant at higher pressures. © 1997 Scripta Technica, Inc Heat Trans Jpn Res, 26(1): 16–29, 1997

Study on Critical Heat Flux in Rectangular Channels Heated From One or Both Sides at Pressures Ranging From 0.1 to 14 MPa

In this study, a quantitative analysis of critical heat flux (CHF) in rectangular heated channels was carried out based on new flow models and the analytical results were compared with existing experimental results at pressures of about 0.1 to 14 MPa with a water mass flux of 3.9 to 28,000 kg/m2s and inlet water subcooling ranging from 0 to 328 K. The flow models proposed for CHF were a completely separated two-phase flow model with a macroliquid sublayer under conditions of comparatively low velocity and zero water subcooling at outlet of the channel and a subcooled boiling flow model with a macroliquid sublayer under the conditions of high water subcooling and high velocity, respectively. It could be shown that the analytical CHF results gave good predictions for over 800 existing experimental results, identifying the effects of predominant parameters as regards CHF.

Critical Heat Flux under Conditions of High Subcooling and High Velocity at Atmospheric Pressure.

A quantitative analysis of critical heat flux (CHF) under high mass flux with high subcooling at atmospheric pressure was successfully carried out by applying a new transition region model for a macro-water sublayer on heated walls to the existing model of a vapor blanket over the macro-water sublayer. The CHF correlation proposed in this study could predict well the experimental data obtained for water mass flux of 940 to 20,300 kg/m2s using circulate tubes 2 to 4 mm in diameter and 30 to 100 mm in length with inlet subcooling of 30 to 90 °C and rectangular channels heated from one side with gaps of 3 to 20 mm, length of 50 to 305 mm, and inlet subcooling of 30 to 77 °C and revealed a unique feature of CHF, namely, that the effects of wall friction of subcooled boiling flow and the velocity of the steam blanket above the macro-water sublayer at atmospheric pressure become the dominant factors while they were not dominant at higher pressures. © 1997 Scripta Technica, Inc Heat Trans Jpn Res, 26(1): 16–29, 1997

Analytical Study on Characteristics of Critical Heat Flux under High Subcooling and High Velocity Conditions.

A quantitative analysis of critical heat flux (CHF) under high mass flux with high subcooling was successfully carried out by applying a new transition region model for a thin liquid sublayer on the heated walls to the existing model of vapor blanket over the thin liquid sublayer. The CHF correlation proposed in this study could predict well experimental data obtained using circular tubes of 2.5 to 3 mm in diameter, 100 to 290 mm in length, 0.34 to 2.6 MPa and 13 to 210°C in inlet subcooling, and rectangular channels of 3.5 mm in gap, 150 mm in length, 0.5 to 3.1 MPa and 13 to 166°C in inlet subcooling, revealing a unique feature that the critical heat flux is proportional to around G0.8, where G is the mass flux, at high mass flux of the dimensionless mass flux G* ranging from 350 to 4700 under the subcooled condition at the exit of the channel.

Analysis of Critical Heat Flux in Two-Phase Thermosyphon. Relationship between Maximum Falling Liquid Rate and Critical Heat Flux.

An analytical study has been performed of critical heat flux of a two-phase thermosyphon, in which a liquid film and a vapor flow in the manner of countercurrent annular flow. The point which can be determined from the three equations of momentum, of its partial derivative with void fraction, and of mass balance in the thermosyphon, is proven to correspond to a maximum falling liquid rate to the thermosyphon. This point, furthermore, becomes identical to the point at which a generated envelope line intersects the mass balance line. The CHF calculated from the maximum liquid rate is found to be in good agreement with the existing CHF data.

Critical Heat Flux of Comparatively Low-Velocity, Upward-Saturated Two-Phase Flow in Vertical Channels.

A quantitative analysis of critical heat flux (CHF) in both vertical circular tubes and rectangular channels under about 0.1 to 14 MPa was successfully carried out by application of the completely separated two-phase flow model to the comparatively low-velocity, upward-saturated two-phase flow, based on existing model of vapor blanket over the thin liquid sublayer on the heated walls at the CHF point, which was originally proposed by Haramura and Katto [Int. J. Heat Mass Transfer, 26-3 (1983), 389-399]. Over 1000 experimental CHF data were compared with analytical results and it was clarified that the analytical results gave good predictions of the existing experimental results of circular tubes of 3.0 to 7.8 mm in diameter and 0.15 to 0.6 m in length at 0 to 300 K and rectangular channels of 1.03 to 12.7 mm in channel gap and 0.15 to 0.94 min channel length at 4 to 328 K of inlet subcooling. The differences in characteristics of CHF between circular tubes and rectangular channels in upward-saturated two-phase How were also identified.

Analysis of critical heat flux during subcooled boiling for finned fuel elements

Experimental and analytical studies were performed to determine the critical heat flux (CHF) during subcooled boiling on finned fuel elements. Tests were conducted in a vertical, concentric-annulus test section consisting of a glass tube containing a finned heater element with either six, eight, or ten longitudinal fins. The phenomena leading to CHF are described and the parametric trends are discussed. A two-dimensional finite-element heat transfer model using the Galerkin method was used to analyse the experimental data to obtain CHF values. A dimensionless correlation was derived to predict the CHF values during subcooled boiling. Over 90% of the predicted CHF values agreed with those obtained from the two-dimensional analysis within ±30%.

Analytical Study of Critical Heat Flux in Upward Saturated Two-Phase Flow in Vertical Rectangular Channels under Atmospheric Pressure.

A quantitative analysis of critical heat flux (CHF) in upward saturated two-phase flow in vertical rectangular channels under atmospheric pressure was successfully carried out by applying the completely separated two-phase flow model to the existing model of vapor blanket over the thin liquid sublayer on the heated walls at the CHF point. The analytical results give good predictions of the existing experimental results in vertical rectangular channels with 1.03 to 5.0 mm channel gap, 40 to 51 mm channel width, 350 to 750 mm channel length and 20 to 88°C inlet subcooling, and identify the effects of predominant parameters on CHF in upward saturated two-phase flow in vertical rectangular channels.

Analytical Study of Critical Heat Flux under Countercurrent Flow Limitation in Vertical Channels.

A quantitative analysis of critical heat flux (CHF) under countercurrent flow limitation (CCFL) or flooding was successfully carried out using the existing experimental results for the vertical circular, rectangular and annular channels, applying the criteria, which was proposed by the author, that the CCFL condition could be determined by maximizing the water mass flux falling down in the vertical channels with respect to the water film thickness and the model of dryout of water film flow at the CHF point. It was clarified that the analytical results give good predictions of the existing experimental results of vertical channels, identifying the factors determining the CHF under the CCFL conditions.